On the word-family MUW and MUSTERION I'd like to offer the assessment of
Walter Burkert , _Ancient Mystery Cults_ (Cambridge and London 1987) pp.
8-9 and footnote 36. Apparently the root is attested in Mycenaean Greek
in the sense of initiation or installation of an official into his office.
"The connection," he says, "with MYW 'to shut one's eyes or lips,' may be
just popular etymology." I say this with regret, because I taught that
connection to my students for years.

On the other hand, that popular etymology had great appeal because the
"things seen and things done" of the mystery cults were quite secret--to
reveal them was to court the penalty of death.